No, I am not. I bet that comp is TRUE, but I don't see COMP as requiring
that the physical world is supervening on numbers (up to
isomorphisms) as
primitives.
So you have to explicitly show what is not valid in the UDA1-8. You miss
something, let us try to find out what.
I am not missing a thing, Bruno. You are missing something that is
obvious to the rest of us.
If someone else can confirm this, and put some light on what Stephen is
saying, I would be pleased.

Bruno, I used to think that you were indeed missing "something that is
obvious to the rest of us". I don't think so any longer, because I
understand now that you are presenting a theory and your arguments
consequently derive strictly from the axioms and assumptions of that
theory. I don't pretend to understand all aspects of that theory of
course, but through discussion and the contrast of ideas I have come a
bit closer than when I started.
I don't know if it will help at all for me to state here my
understanding of what might motivate the theory in the first place,
but I'll try. Firstly, as you have so often said, the
informational/computational theory of mind (CTM) is more or less the
default assumption in science. Indeed this conclusion seems almost
unavoidable given that brain research seems to imply, more or less
unambiguously, the correlation of mental states with relations,
rather than relata. However, CTM in its uncritically-assumed form
continues to be combined with the additional assumption of an
Aristotelian primitively-physical state of affairs. This leads
directly either to denialism of the first-person, or alternatively to
some ill-defined species of property dualism. These consequences by
themselves might well lead us to reject such primitive-physicalism as
incoherent, even without an explicit reductio ad absurdum of the
unambiguous association of conscious states with "physical
computation". Either way, in order to retain CTM, one is led to
contemplate some form of neutral monism.
The question of what form such a "neutral" theory should take now
arises. Since the theory is explicitly *computational*, the axioms
and assumptions of such a theory should obviously be restricted to the
absolute minimum necessary to construct a "computational universe" (in
the traditional sense of "universe") or rather to indicate how such a
universe would necessarily construct itself, given those axioms and
assumptions. The basic assumption is of a first-order combinatorial
system, of which numbers are the most widely-understood example.
Given the arithmetical nature of such a universe, construction and
differentiability of composite entities must necessarily derive from
arithmetical assumptions, which permits the natural emergence of
higher-order structural integration via the internal logic of the
system. Of particular note is the emergence in this way of
self-referential entities, which form the logical basis of
person-hood.
Since the reality of first-person localisation is not denied in this
theory (indeed the theory positively seeks to rationalise it), the
system is not posited as having merely third-personal status, but as
possessing a first-person self-referential point-of-view which is
associated with consciousness. Perhaps it is this aspect of the
theory which is the most tricky, as it cuts across a variety of
different intuitions about consciousness and its relation to the
phenomena it reveals. For rather than positing a primitively-physical
universe which "instantiates" conscious states, the theory must
reverse the relation and posit conscious states that "instantiate"
physical phenomena. In so doing, it exposes itself to empirical
refutation, since those phenomena must be, at least, consistent with
ordinary observation (although they also predict, in the limit,
observations of high improbability).
It is this last issue of instantiation which seems to be one of main
bones of contention between Stephen and yourself, though I'm not sure
why this is the case. From my own perspective, unsophisticated though
it may be, it seems reasonable that the emergence of "truly physical"
phenomena should indeed be the result of "personal instantiation" in
the conjunction of consciousness and computation. After all, when do
questions as to what is "truly physical" emerge, other than in the
context of what is "truly experiential"? The rest is calculation.
David

Dear David,
Does my claim that our primitive ground must be neutral with respect to
any properties make any sense? It like the zero of arithmetic from which
we can extricate any set of positive and negative quantities in pairs
such that their sum is equal to zero. What I see in Bruno's
interpretation of COMP is that it permits for the primitive to have a
set of properties (numbers and + and *) to the exclusion of its
complementary opposites. Since this is a violation of neutrality, thus I
see a fatal flaw in Bruno's Ideal monist interpretation.
Onward!
Stephen

One can wonder what is the most "general" theory that we can postulate
to explain our existence. Tegmark postulates all of consistent
mathematics, whatever that is, but is 'all of consistent mathematics'
consistent in itself? Schmidhuber postulates something much less, just
the UD, but strangely forgets the first-person or the what the
implementation substrate of that UD would be (and resorts to a Great
Programmer to hand-wave it away).
Before reading the UDA, I used to think that something like Tegmark's
solution would be general enough and sufficient, but now I think 'just
arithmetic' (or combinators, or lambda calculus, or ...) or is
sufficient. Why? By the Church-Turing Thesis, these systems posses the
same computability power, that is, they all can run the UD. Now, if we
do admit a digital substitution, all that we can experience is already
contained within the UD, including the worlds where we find a physical
world with us having a physical body/brain (which exist computationally,
but let us not forget that random oracle that comes with 1p
indeterminacy). If we are machines, then we can only experience finite
amount of information given some finite interval of time, some of this
information may be incompressible, due to 1p indeterminacy, thus we
could experience "reals" in the limit, despite there only being finite
computations at any given time. This essentially means that any
mathematical object which can be described in Tegmark's "Ultimate
Ensemble" and that can contain us, is already part of the 1p experiences
of those existing within the UD and we can look at 1p experiences, as
well as the UD* trace as being part of the greater "arithmetical" truth
(or any other theory with equivalent computational power, by the
Church-Turing Thesis).

This is why I think "arithmetic" is as good as any for a neutral
foundation, and we cannot really distinguish (from the inside) between
these foundations by the CTT. However, there might be other possible
foundations, if you wish to postulate concrete infinities, but even if
they existed, how could we tell them apart, it doesn't seem to be
possible for someone admitting a digital substitution, which has a
finite mind (at any finite point in time). If you can show that those
other foundations are necessary and they affect our
measure/continuations, or that concrete infinities are involved in the
implementation of our brain, it could prove COMP wrong.
There is another problem with taking a set theory as foundational rather
than arithmetic - some set theories have independent axioms and they can
be extended by adding either an axiom or its negation, and they result
in different set theoretical truths. This doesn't really happen with
computation - if there's anything absolute in math, it's computation
(although different theories about what arithmetic is will result in
different things the theory can talk about, but it won't make
computation any less absolute).

As a side-note, I don't see why the primitive physical world is
necessary, from the 1p, we can only know that we have senses and from
the senses we can infer the existence of the external world. If
consciousness is how some (possibly self-referential) arithmetical (or
computational) truth feels from the inside, it does not seem impossible
that there would not be computations representing some physical (just
not primitive) world and that world would contain us and our
bodies/brains, and the existence of such computations would be a theorem
in arithmetic.

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